This paper introduces a novel 6D dynamic system derived from modified 3D Lorenz equations of the second type using state feedback control. While the original 3D equations are formally simpler than the classical Lorentz equations, they produce topologically more complex attractors with a two-winged butterfly structure. The proposed system contains the fewest terms compared to existing literature. These terms comprise two cross-product nonlinearities, two piecewise linear functions, six linear terms, and one constant. The new 6D hyperchaotic system exhibits a rich array of dynamic characteristics, including hidden attractors and dissipative behavior. A thorough dynamic analysis of this system was performed. In particular, bifurcation diagrams were constructed, Lyapunov exponents and dimensions were calculated, and multistability and offset boosting control were analyzed to understand the systems behavior further. An electronic circuit of the 6D hyperchaotic two-winged butterfly system was developed in the Multisim computer environment. The designed electronic circuit showed excellent agreement with the simulation results of the new 6D dynamic system. Synchronization of two identical 6D hyperchaotic systems was achieved using the active control method.